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HAECCEITISM, CHANCE,
AND COUNTERFACTUALS
Boris Kment
Abstract. Anti-haecceitists believe that all facts about
specific individuals—such
as the fact that Fred exists, or that Katie is tall—globally
supervene on purely
qualitative facts. Haecceitists deny that. The issue is not only
of interest in itself,
but receives additional importance from its intimate connection
to the question of
whether all fundamental facts are qualitative or whether they
include facts about
which specific individuals there are and how qualitative
properties and relations
are distributed over them. Those who think that all fundamental
facts are
qualitative are arguably committed to anti-haecceitism. The goal
of this paper is
to point out some problems for anti-haecceitism (and therefore
for the thesis that
all fundamental facts are qualitative). The article focuses on
two common
assumptions about possible worlds: (i) Sets of possible worlds
are the bearers of
objective physical chance. (ii) Counterfactual conditionals can
be defined by
appeal to a relation of closeness between possible worlds. The
essay tries to show
that absurd consequences ensue if either of these assumptions is
combined with
anti-haecceitism. Then it considers a natural response by the
anti-haecceitist,
which is to deny that worlds play the role described in (i) and
(ii). Instead, the
reply continues, we can introduce a new set of entities that are
defined in terms of
worlds and that behave the way worlds do on the haecceitist
position. That allows
the anti-haecceitist to formulate anti-haecceitist friendly
versions of (i) and (ii) by
replacing the appeal to possible worlds with reference to the
newly introduced
entities. This maneuver invites an obvious reply, however. If
the new entities are
the things that play the role we typically associate with
worlds, as partially
described by (i) and (ii), then it is natural to conclude that
they really are the
entities we talk about when we speak of worlds, so that
haecceitism is true after
all.
Imagine a symmetrical world w where nothing exists except two
qualitatively
indistinguishable motionless fundamental particles, A and B, in
otherwise empty space-
time.1,
2 Both particles have always existed and will always continue to
exist. Nothing in
this world ever changes. Let t be any point of time. It’s surely
true that
For helpful comments and discussion, I am indebted to David
Baker, Ross Cameron, David Chalmers,
Shamik Dasgupta, John Divers, Andy Egan, Adam Elga, Delia Graff
Fara, Liz Harman, Reina Hayaki, Sam
Liao, Martin Lin, Alyssa Ney, Jill North, Howard Nye, Laurie
Paul, David Plunkett, Ted Sider, Bruno
Whittle, Robbie Williams, to two anonymous referees for
Philosophical Review, to the participants of
graduate seminars I taught at the University of Michigan and
Princeton University, and to the audiences of
talks I gave at Auckland, Sydney, the 2008 Australasian
Association of Philosophy conference, the 2011
bkmentText BoxPublished in Philosophical Review 121, 2012, pp.
573 -609.
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2
(1) It is (metaphysically) possible that A disappears at t,
while B continues to exist
forever.
Hence, there is a possible world w1 that meets the following
description.3
w1: Before t, everything happens exactly the way it does in w.
Then at t, A
disappears, while B continues to exist forever.
The following claim is surely true as well:
(2) It is (metaphysically) possible that B disappears at t,
while A continues to exist
forever.
So, there’s surely a possible world w2 meeting the following
description.
w2: Before t, everything happens exactly the way it does in w.
Then at t, B
disappears while A continues to exist forever.
Most philosophers would agree with judgments (1) and (2), and
would therefore agree
that there is both a possible world that meets our description
of w1 and a possible world
that meets our description of w2. What is much more
controversial, however, is whether
the two descriptions single out different worlds, or whether
they are merely different
descriptions of the same world. Note that w1 and w2 are
qualitatively indistinguishable
Rocky Mountains Philosophy Conference, Geneva, Manchester,
Stirling, Leeds, and the 2012 Central
APA. Research for this paper was assisted by an ACLS/Charles A.
Ryskamp Fellowship from the
American Council of Learned Societies. I am grateful for their
support. I am equally indebted to the
National Endowment for the Humanities for support (Grant Number
FA-54195-08) during the period when
a substantial initial part of the research for this paper was
done. (Any views, findings, conclusions, or
recommendations expressed in this paper do not necessarily
reflect those of the National Endowment for
the Humanities.)
1 The example is a variant of an example due to Robert Adams
(1979), and is reminiscent of the well-
known case of the two spheres that Black gives in his (1952).
However, Black’s concern was not with the
modal thesis of anti-haecceitism, but with the thesis of the
identity of indiscernibles.
2 By saying that the two particles are qualitatively
indistinguishable I mean that they share all purely
qualitative properties, where a purely qualitative property is,
roughly speaking, one whose instantiation by
a certain individual is in no way a matter of which individual
it is or which individuals it is related to. (This
sense of ‘qualitative’ is different from the sense of the same
word that contrasts with ‘quantitative.’) Note
that it’s compatible with the qualitative indistinguishability
of the two particles that they have different
locations, provided that the two locations themselves are
qualitatively indistinguishable.
3 More precisely: at w, there’s a possible world w1 that meets
this description. Some philosophers,
typically actualists, believe that possible worlds can be
contingent existents. On such a view, w1 may not
actually exist.
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(that is, the same qualitative facts obtain at both of them). w2
is just w1 turned around by
180 degrees, as it were. If there’s a difference between them,
then it can only concern the
question of which particle it is that disappears and which
particle it is that remains; the
particle that disappears in w1 is the one that continues to
exist in w2, and vice versa. And
philosophical opinion is divided on the question whether two
worlds can differ only in
how qualitative roles are distributed over individuals, without
differing qualitatively.
If you think that the answer to this question is affirmative,
then you are a ‘haecceitist’
in the sense in which I will be using the term.4 Haecceitists
believe that there is more to a
possible world than its qualitative character. There is, in
addition, the question of which
individual plays which qualitative role, and the qualitative
nature of a possible world
need not determine the answer to this question. By contrast, if
you think that possible
worlds cannot differ in what’s true at them about specific
individuals without differing
qualitatively, then you are an ‘anti-haecceitist.’
Anti-haecceitists believe that what is true
of a certain individual at a specific world is completely
determined by the world’s
qualitative character and the features of the relevant
individual.5
How is that supposed to work? The standard anti-haecceitist
answer appeals to the
notion of a counterpart. An individual a is P at world v (or: v
represents a as being P6, 7
—
4 The term, of course, is due to Kaplan (1975, 722f.). For a
very useful explanation of haecceitism, see
Lewis (1986b, ch. 4).
5 Anti-haecceitism says that two worlds v and v* that are
qualitatively alike don’t differ in what’s true at them concerning
specific individuals. As Lewis has pointed out, that doesn’t entail
that v and v* are
identical (1986b, 224). It’s consistent with anti-haecceitism
that there are qualitatively indistinguishable
worlds that are not identical, though anti-haecceitism entails
that such worlds cannot differ at all in what’s
true at them. Anti-haecceitists who allow for this possibility
might say that there could be more than one
world that meets our description of w1, and more than one world
meeting our description of w2. But they
would still say that any world satisfying the first description
also fits the second, and vice versa. The two
descriptions don’t single out different worlds. That’s where the
anti-haecceitist and the haecceitist disagree.
For the sake of simplifying the discussion, I will often write
as if the anti-haecceitist was committed to
the identity of qualitatively indiscernible worlds. But nothing
will hang on it. The discussion could easily
be reformulated so as to use only the weaker assumption that the
anti-haecceitist is committed to the thesis
that qualitatively indiscernible worlds are completely
indiscernible in what’s true at them.
6 … or, as Lewis expresses it in his (1973): individual a
‘vicariously satisfies’ the open sentence ‘x is P’
at world v.
7 I am here using ‘represent’ in a technical sense. To say in
this sense that w represents that P is simply to say that the claim
that P is true at w in a technical sense of ‘true at’ that is
specific to the theory of
modality. (And if P is a claim about specific individuals, then
by counterpart-theoretic lights, the claim that
w represents that P is merely convenient shorthand for a certain
counterpart-theoretic claim.) I think that
this sense of ‘represent’ may not be the same as the sense in
which we talk about, for instance, mental or
linguistic representation. The term ‘true at (a world)’ is in a
similar position to ‘represent.’ I don’t claim
that it is related in any simple and straightforward way to any
ordinary, pre-theoretical notion of truth.
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I will use the two phrases interchangeably) just in case v
contains an individual that is a
‘counterpart’ of a, that is to say, which stands to a in the
right kind of similarity relation,
and that is P.8 Example: You are a philosopher, but you could
have been a professional
tennis player. That is to say that some possible world
represents you as a tennis player.
For the counterpart theorist, that is to say that some possible
world contains a counterpart
of you—someone standing in the right similarity relation to
you—who plays tennis for a
living.9
The anti-haecceitist can agree, then, that we can describe other
possible worlds by
referring to specific individuals, as when we say that you are a
tennis player at this or that
world. But that’s just a complex and sophisticated method of
describing what purely
qualitative facts obtain at that world. We are describing these
facts by comparing the
qualitative features of the other world’s denizens to those of
the inhabitants of our world.
We are, as it were, using the individuals of our world as a
reference frame for describing
the qualitative character of the other world. (Sometimes there
are two equally good ways
of doing this. The anti-haecceitist would say that that’s what
happens in the example of
the two particles. The very same world meets our description of
w1 and our description of
w2. For the particle that disappears at that world is a
counterpart of both A and B, and the
same is true of the particle that remains. That’s why the world
can be described as one
where A disappears while B remains, or as one where B disappears
while A remains.)
Is it possible to be an anti-haecceitist without endorsing
counterpart theory? Not, as
far as I can see, without significant cost. Surely,
anti-haecceitists want to be able to say
that (1) and (2) are both true in our example, and hence that
there are possible worlds that
meet our descriptions of w1 and w2. At the same time, they need
to say that the two
8 Some counterpart theorists may prefer not to state the fact
that a has a counterpart in w that is P by saying
that a is P at w, or that ‘a is P’ is true at w, since on this
account the concept of truth at a world may not
behave in quite the way it is often thought to behave. (For
example, we are used to saying that a sentence S
is necessary just in case S is true at all possible worlds. When
combined with the present conception of
truth at a world, that entails that ‘a is P’ is necessary just
in case every world contains a counterpart of a
that is P. Counterpart theorists may not accept that, but may
prefer to say, e.g., that the sentence is
necessary just in case all counterparts of a are P.) It seems to
me, however, that there is no harm in using
‘true at’ in the way described, provided we are careful not to
assume that the concept it expresses plays
exactly the role most commonly ascribed to it.
9 For expositions of Lewis’s counterpart theory, see Lewis
(1968, 1971, 1973, 1986b). For other
versions of counterpart theory, see Forbes (1982, 1987, 1990),
Ramachandran (1989, 1990a, 1990b). For a
classic discussion, see Hazen (1979). For some more recent
discussion, see Dorr (2005, n.d.); Fara &
Williamson (2005); Fara (2008, 2009).
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descriptions single out the same world, so they need an account
of de re modal talk
according to which one and the same world can be correctly
described in either way: by
saying that particle A disappears while particle B doesn’t, and
by saying that B disappears
while A doesn’t. And to my knowledge, counterpart theory is the
only account ever
developed that allows us to describe one and the same world in
both of these ways
without contradiction. I will assume in what follows that all
parties to the debate agree
that we should accommodate the intuition that underlies our
judgment that (1) and (2) are
true in the example, and will therefore restrict my attention to
those versions of anti-
haecceitism that endorse counterpart theory.
I will not assume, however, that every counterpart theorist has
to be an anti-
haecceitist. Some philosophers have proposed, or at least
discussed, non-qualitative
counterpart theory, that is, theories according to which the
extension of the counterpart
relation is not completely determined by purely qualitative
similarities between
individuals. Variants of such a view are described, for example,
in Lewis (1986b, scts.
4.4 – 4.5), Fara (2008) and Dorr (n.d.). Such views are usually
haecceitist. They fall
outside the scope of my paper, since my target is
anti-haecceitism (and the concomitant
theory of qualitative counterparts), not counterpart theory as
such. I do not claim that my
arguments apply to non-qualitative counterpart theory.
The dispute between haecceitists and anti-haecceitists is not
only of interest in itself. I
think that it derives additional importance from its intimate
connection to a number of
further issues in metaphysics, one of which I will discuss in
section 1. Previous
discussions of haecceitism have most often focused on one or
another of a restricted
range of issues. Some authors, for example, attempted to
evaluate the two opposing
positions in light of pre-philosophical intuitions about the
identity or distinctness of
possibilities.10
Although I cannot argue the point here, I suspect that such
considerations
yield at best a draw. Other discussions have centered on the
difficulties that counterpart
theorists face when trying to give an account of how the
actuality operator works. The
problem was pointed out by Allen Hazen (1979), and a complex
debate ensued, with
several revisions of counterpart theory being proposed and new
variants of the problem
10 For discussions of these intuitions, see, for example, Adams
(1979), Lewis (1986b, ch. 4).
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formulated that affect these new versions (Forbes (1982, 1985,
1987, 1990),
Ramachandran (1989, 1990a, 1990b), Fara & Williamson (2005),
Fara (2008); also see
Dorr (n.d.)). The dialectic here may be ongoing. I will not,
however, jump into the fray to
determine who will ultimately win this debate. For I think that
there are other formidable
difficulties confronting the anti-haecceitist. After some
stage-setting in section 2, I will
center on two problems that have not received a lot of attention
so far, one in the theory
of chance (section 3), and one in the theory of counterfactual
conditionals (section 4).
Section 5 explores some strategies that an anti-haecceitist
could employ to respond to
these problems, and argues that they are likely to confront
significant challenges.
1. A reason to care about the haecceitism dispute: the question
whether reality is at
bottom purely qualitative
I take it to be an important task of the metaphysician to find
out what reality looks like at
the most fundamental level. Among other things, we want to find
out how rich an
ideology and ontology we need in order to give a complete
description of the
fundamental facts about the world. There is no lack of strong
opinions about this topic.
Consider physicalism. On one interpretation, this is the thesis
that all fundamental facts
are physical facts. All other facts are grounded in the physical
facts. The debate about
haecceitism is intimately connected to another thesis with a
similar structure: the thesis
that all fundamental facts are qualitative; that is, that they
are facts about the pattern of
instantiation of properties and relations that are purely
qualitative (in the sense that their
instantiation by certain individuals is in no way a matter of
which specific individuals
these are or which specific individuals they are related to). I
will call this thesis ‘anti-
individualism.’ The opposing view, individualism, holds that the
fundamental facts
include in addition what I will call ‘individualist’ facts:
facts about which specific
individuals there are, and how the qualitative properties and
relations are distributed over
specific individuals.11
To get the contrast between the two positions into clearer
focus, let’s suppose that we
had at our disposal a language all expressions of which are
purely qualitative. It has no
11 I am borrowing the term ‘individualism’ from Dasgupta
(2009).
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names for individuals, and no other expressions (like
‘pegasizes,’ ‘Socrateity,’ ‘Marxist’
or ‘French’) that make overt or covert reference to specific
individuals. All of its
predicates and relation symbols express properties and relations
that are qualitative. But
the resources of the language are otherwise unlimited. It can
describe every qualitative
fact. The anti-individualist believes that such a language would
suffice to give a complete
description of all of fundamental reality. The individualist
denies that.
Anti-individualists reject fundamental individualist facts. But
they are free to accept
that individuals exist. They may even include individuals in
their fundamental ontology;
that is to say, they may hold that, in stating the fundamental
facts, we need to quantify
over individuals. Some of the sentences stating fundamental
facts might, for example, be
of the form ‘(x)(Px)’ or ‘(x)(y)(Rxy).’ These sentences are,
after all, cast in a purely
qualitative language. The anti-individualist just needs to hold
that when stating the
fundamental facts, we cannot add, after saying that there is an
individual with such-and-
such qualitative features: and that individual is a. Such a view
would allow individuals
into our fundamental ontology, and yet be anti-individualist in
my sense. The view could
perhaps be stated by saying that, even fundamentally speaking,
there are indeed
individuals, but there are no fundamental facts about which
individual any one of them is.
Individuals are, as it were, mere anonymous loci of
instantiation of qualitative properties
and relations, nameless pegs on which we can hang these
properties and which we can
connect by these relations. They are individuals without
individuality.12,
13
12 Some philosophers (for example Rosen, (2010) and personal
communication; for an interesting
discussion, see also Fine (n.d., §7)) are attracted to the
principle that all existential facts must be grounded
in their instances. For example, if it is a fact that something
is F, then that fact must be grounded in some
specific instance of this existential generalization, that is,
in some fact of the form a is F. As Gideon Rosen
pointed out to me, anti-individualists who include individuals
in their fundamental ontology need to give up
this principle. For these philosophers believe that there are
fundamental facts of the form ‘there is an x that
is P’. Since fundamental facts aren't grounded in other facts,
it follows that these existence facts aren't
grounded in their instances. I happen to believe that there are
independent reasons for abandoning the
principle that all existential facts are grounded in their
instances (though I cannot argue the point here), so I
don’t count this as a serious cost of anti-individualism with
fundamental individuals.
13
It’s worth noting that anti-individualists who accept
individuals into their fundamental ontology will
most likely deny that the operator ‘it’s a fundamental fact
that’ commutes with the existential quantifier.
For they accept that there are truths of the form it’s a
fundamental fact that there is an individual x such
that Fx, but will probably deny that that entails there is an
individual x such that it’s a fundamental fact
that Fx (for the latter claim appears to entail that there are
fundamental individualist facts). (Thanks to an
anonymous referee for Philosophical Review for pointing this
out.)
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Just as anti-individualism doesn’t commit you to excluding
individuals from your
fundamental ontology, it doesn’t commit you to the identity of
qualitatively
indiscernibles. The anti-individualist could hold that a
complete description of
fundamental reality includes the claim that
(3) (x)(y)(Φ(x) & Φ(y) & x ≠ y),
where ‘Φ’ incorporates a complete description of the qualitative
features (including
relational ones) of the two individuals. (3) is, after all, cast
in purely qualitative terms, so
that the claim that it states a fundamental fact doesn’t violate
the principle that all
fundamental facts are qualitative. In other words, the
anti-individualist can allow that two
individuals are qualitatively indistinguishable, but
distinct.
A thesis (like physicalism or anti-individualism) that is of the
form ‘all facts are
grounded in the A-facts’ or ‘all fundamental facts are A-facts’
is connected in interesting
ways to a corresponding supervenience thesis. Consider
physicalism again. That thesis is
widely thought to be tied in important ways to a thesis of
global supervenience, though
it’s controversial what the relevant supervenience thesis is.
The simplest global
supervenience thesis in this area is the claim that
(4) All facts globally supervene on the physical facts,
that is, that there are no two possible worlds that are alike in
all physical facts, but differ
in other ways. It is widely assumed, though, that the
physicalist is not committed to a
thesis that strong. Most physicalists, after all, take
physicalism to be a contingent truth.
They needn’t deny that there are possible worlds containing
immaterial spirits, for
example. (They just deny that the actual world is like that.)
And they can allow that there
are two immaterial-spirit worlds that are physically alike but
differ in spiritual facts,
which would be a counterexample to (4). The supervenience thesis
connected to
physicalism must therefore be weaker than (4), and there are
different ways in which
physicalists can weaken (4).14
Following Lewis's statement of materialism (1983), for
example, they may restrict the supervenience thesis to worlds
that contain no instances of
14 For some well-known strategies for weakening (4), see Lewis
(1983), Jackson (1998, 12), Chalmers
(1996).
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natural properties that are “alien to the actual world,” that
is, natural properties that aren’t
instantiated in the actual world, and that aren’t conjunctions
of, or structural properties
constructed from, natural properties instantiated in the actual
world.15
(The immaterial-
spirit worlds then no longer present a problem, since by
physicalist lights they contain
instances of alien natural properties.)
Now, it is a good question how physicalism relates to the
suitably qualified thesis of
global supervenience. Some philosophers have assumed that
physicalism is that
supervenience thesis. Other philosophers have argued that the
most interesting thesis of
physicalism is much stronger than the supervenience
thesis.16
In any case, though, it
seems very plausible, and it is widely assumed, that physicalism
entails the
supervenience thesis.
What we said about physicalism also holds, mutatis mutandis, for
anti-individualism.
We should expect that this view commits its proponent to a
supervenience thesis (even if
it’s not identical with any supervenience thesis). The simplest
supervenience thesis in the
area is the claim that all facts globally supervene on the
purely qualitative facts, that is,
that there are no two possible worlds that are qualitatively
indistinguishable but differ in
other ways, namely in what’s true at them concerning specific
individuals. And that, of
course, is just anti-haecceitism.
Are anti-individualists committed to the unqualified thesis of
anti-haecceitism? That
depends at least in part on whether they take anti-individualism
to be a necessary truth. If
they do, that is, if they think that it’s true in all possible
worlds that all fundamental facts
are purely qualitative, then they are likely to accept the
unrestricted version of the anti-
haecceitist supervenience thesis. But they may instead take the
truth of anti-individualism
to be contingent (for example, if their anti-individualism is
motivated by empirical results
about the chance distribution over possible outcomes of quantum
coin tosses, or by the
apparent undetectability of individualist facts17
). Then they may want to add a restriction
to the supervenience thesis, just as proponents of contingent
physicalism qualify their
thesis of the global supervenience on the physical. Roughly
speaking, if w and w* are two
15 Lewis (1983).
16
See Horgan (1993) for discussion. For relevant discussion, also
see Kim (1993, 1998, 2005).
17
See, for example, Teller (2001), Dasgupta (2009).
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possible worlds where fundamental reality isn’t richer than in
the actual world as far as
individuality is concerned, w and w* don’t differ without
differing qualitatively. That’s
not very precise of course, but for our purposes it won’t be
important to give a more exact
formulation, since (for reasons to be considered presently) the
details don’t matter much
for my purposes.
Anti-individualism paints a more parsimonious picture of what
reality is like at the
most fundamental level than individualism does. So, there is a
possible Occamist
motivation for being an anti-individualist, and hence for
endorsing anti-haecceitism, or at
least the restricted version of anti-haecceitism that is
entailed by the most plausible
version of anti-individualism. Conversely, if it is possible to
show that anti-haecceitism,
or a suitably restricted version of it, is untenable, then that
would vindicate individualism.
In sections 3 and 4 I will consider arguments aimed to show that
we are in theoretical
trouble unless we accept the existence of pairs of worlds that
are qualitatively
indistinguishable but differ in what’s true at them concerning
specific individuals. I
believe that there is absolutely no reason for thinking that,
when it comes to the structure
of individuality, fundamental reality is somehow richer in the
worlds that figure in my
examples than in the actual world. I therefore suspect that, if
the arguments in sections 3
and 4 carry the day, then the examples figuring in these
arguments are counterexamples
even to a suitably restricted version of anti-haecceitism (no
matter what the details of the
restriction are), and therefore present a problem for the
anti-individualist.
That claim needs to be qualified in one way, however. I
mentioned that anti-
individualism as such doesn’t commit you to excluding
individuals from your
fundamental ontology, or to endorsing the identity of
qualitatively indiscernibles. But
some versions of anti-individualism embrace these commitments
anyway. An example is
the bundle theory of individuals, which holds that,
fundamentally speaking, all that exists
are qualitative properties. Individuals are bundles of these.
This view rejects fundamental
individuals and arguably precludes the possibility of distinct
but qualitatively
indistinguishable individuals. Another example is the
sophisticated view recently
proposed by Shamik Dasgupta,18
which also excludes individuals from fundamental
18 Dasgupta (2009).
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ontology, at least as far as the material world is concerned
(though it doesn’t endorse the
identity of qualitatively indiscernibles). The arguments in
sections 3 and 4 won’t apply to
versions of anti-individualism that endorse the identity of
qualitatively indiscernibles, and
it is open to question whether they, or suitable variants of
them, apply to views that deny
that the fundamental entities include individuals (a question
that I will have no space to
consider in this paper). It also seems to me, however, that
views of these two kinds depart
more strongly from pre-philosophical opinion than we need to in
order to be anti-
individualists. More conservative forms of anti-individualism
are directly in my firing
line.
With the distinction between individualism and
anti-individualism clearly in mind, the
reader may be tempted to raise an objection. In the
introduction, I described the two-
particle world by saying things like: it’s true at this world
that A could have decayed. And
I said that I expected widespread agreement that there is a
world that meets that
description. But the claim that it’s possible that A decays may
sound like it’s stating an
individualist fact (the sentence may seem to say that there’s a
particle that could have
decayed and also to tell us which particle that is, namely A).
Consequently, some readers
may suspect that those who take anti-individualism to be a
necessary truth shouldn’t
accept that there is a world that meets my description since,
fundamentally speaking at
least, no possible world contains individualist facts.
In response, I say: think of the letters ‘A’ and ‘B’ in my
description of w, not as proper
names for the two particles, but as variables bound by an
existential quantifier at the
beginning of my description. In other words, my description
should be interpreted thus:
(5) There is a particle A and a particle B that have
such-and-such qualitative
properties and stand in such-and-such qualitative relations,
such that it’s possible
for A to decay while B doesn’t, and it’s also possible for B to
decay while A
doesn’t.
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With ‘A’ and ‘B’ understood in this way, (5) is cast in purely
qualitative terms, and even
those who take anti-individualism to be a necessary truth should
accept that there are
possible worlds where (5) is true.19
It’s important to take this point fully on board since the
examples considered in the
rest of this essay will be very similar to the two-particle
case. In each case, I will describe
a possible world involving various individuals, assign labels to
these individuals (‘A’ and
‘B’, ‘Fred’ and ‘Twin-Fred’), and then use these labels to say
that such-and-such is true
of these individuals at that world (for example, that it's true
at the world that such-and-
such would have happened to these individuals if this or that
had been the case, or that
the chance is p that such-and-such will happen to them). In each
case, that should be
understood as the claim that a certain existentially quantified
claim is true at the world,
with the labels being variables that are bound by the
quantifiers at the beginning of that
quantified claim.
2. Preliminaries
Before we can start to discuss the difficulties for
anti-haecceitism, some preliminaries are
needed. Whether an individual x is a counterpart of individual y
depends whether x and y
stand in the right similarity relation to each other. There are
different ways of making this
idea more precise. David Lewis, for example, offers the
following definition: a* in world
v is a counterpart of a just in case a* has a certain minimum
degree of overall similarity
to a in its purely qualitative properties, and nothing in v is
more qualitatively similar
overall to a than a*.20
Another natural definition, broader and simpler, omits the
second
clause: a* is a counterpart of a just in case a* is sufficiently
qualitatively similar overall
to a.
19 To give an account of what makes (5) true at these worlds,
the necessitarian anti-individualist needs to
appeal to counterpart theory. (5) is true at w because it’s true
at w that
There’s a particle A and a particle B that have such-and-such
qualitative properties and stand in
such-and-such qualitative relations, such that there’s a
possible world w1 that contains a
counterpart of A that decays and a counterpart of B that doesn’t
decay, and there’s also a possible
world w2 that contains a counterpart of B that decays and a
counterpart of A that doesn’t decay.
20
Lewis (1973, 39).
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13
I said that counterparthood is a relation between individuals
that may inhabit different
possible worlds. But how literally we can take talk about
individuals in other worlds
depends on our theory of worlds. On Lewis’s realist account,
worlds are, to simplify a
little, spatio-temporally extended objects, many of them filled
with material things like
you.21
On this conception, talk of a world’s constituent individuals
can be taken in the
most literal sense. But most philosophers would reject this
realist picture, in favor of
thinking of worlds as abstract entities. Then talk of
constituents of a world may need to
be construed differently. For the purposes of illustration,
consider what Lewis has called
‘linguistic ersatzists,’ that is, philosophers who regard worlds
as sentences or sets of
sentences of a special universal language.22
Linguistic ersatzists who want to be an anti-
haecceitists could build worlds using the resources of a
language that contains no singular
constants and whose predicates are purely qualitative. To fix
ideas, let us assume that
they think of a world as a long Ramsey sentence, a sentence that
starts with a long string
of existential quantifiers, followed by an open sentence
containing all the variables bound
by these quantifiers and no other singular terms. The sentence
must be constructed so as
to give us a complete qualitative description of reality. One
world, the ‘actual’ one, is a
wholly true description of reality, all other worlds depart to
various degrees from the
truth. Each world is associated with many qualitative roles of
individuals, one for each of
the variables bound by the initial quantifiers of the Ramsey
sentence. All talk about the
constituents of a world can be spelled out as talk about these
qualitative roles. We can
take the ‘constituent individuals’ of a world u to be pairs ,
where v is one of the
individual variables occurring in the Ramsey sentence u.
(Adapting a common term, we
can call these pairs ‘centered worlds.’) We can define a
counterpart relation between
these centered worlds. If we accept the definition of
counterparthood that Lewis gave in
his (1973), we can say that is a counterpart of just in case the
qualitative
role given by is sufficiently similar to the one given by and at
least as
similar to the latter as the qualitative role of any other
individual in u. (By omitting the
second clause, we obtain a new version of the simpler
alternative definition of the
counterpart relation.) By extension, we can also speak of the
constituent individuals of
21 Lewis (1986b, ch. 1).
22
See Lewis (1986b, sct. 3.2).
-
14
worlds (that is, of centered worlds) as being counterparts of
concrete individuals like you
and me. is a counterpart of you just in case the qualitative
role given by
stands in the right similarity relation to your own qualitative
role. World u represents you
as having property P just in case there is a constituent
individual of u that is your
counterpart, and being P is part of the qualitative role given
by .
3. The role of possibilities in the theory of chance23
One part of the theoretical role of possibilities concerns the
theory of objective physical
chance. At any given time, different possible future histories
of the universe have
different chances. We can think of the chance distribution at
time t as a probability
measure on the set of metaphysically possible worlds. Let us
call the set of possible
worlds that are like the actual world up to time t and follow
the actual laws thereafter ‘the
set of possibilities open at t,’ or ‘OPt,’ for short. (The set
of worlds not in OPt has
probability measure zero.) Under determinism, OPt contains
exactly one world, which
has a chance of 1 of being actualized. Under indeterminism,
chances may be spread out
more widely over worlds.
Instead of applying predicates of the form ‘has an X% chance at
time t’ to (sets of)
possible worlds, our discourse about chance often makes use of a
family of sentence
operators of the form ‘there’s a chance of X% at time t that P.’
(I will sometimes
abbreviate this as ‘cht(P) = X%.’) The two locutions are
connected by the simple
principle that
(6) The chance that P is x just in case the chance measure of
the set of possible
worlds where it’s true that P is defined and equals x.
(The relativization to a time has been left implicit for the
sake of simplicity.) For
example, the chance that it will rain in New York City tomorrow
equals the chance
measure of the set of those worlds where it’s true that it will
rain in New York City
tomorrow.
23 For an influential discussion of counterpart theory and some
of its implications for the theory of
probability, see Kripke (1980, 16ff.).
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15
We often use sentences of the form ‘the chance that a is F
equals x.’ (6) tells us that
such a sentence is true iff the chance measure of the set of
worlds where it’s true that a is
F equals x. By anti-haecceitist lights, these are the worlds
where some counterpart of a is
F. In general, it seems that the anti-haecceitist has to say
that
(7) The chance that Φ(a) equals the chance measure of the set of
possible worlds that
contain a counterpart of a that satisfies ‘Φ(x).’24
This view, however, has numerous problematic consequences. We
can bring them into
clear focus by considering the example of a possible world w
that meets the following
description:
(8) The universe is indeterministic, and up to t it consists of
two indistinguishable
halves, Lefty and Righty, arranged in such a way that (up to t)
the universe is
perfectly symmetrical. (By coincidence, all random processes up
to t have the
same outcomes in the two halves.) There is a type of particle,
called the ‘X
boson.’ The laws allow for the possibility that an X boson
decays and disappears,
but not for the possibility that a new X boson is created (the
number of X bosons
can diminish over time, but never increase). There are exactly
two X bosons at t,
A in Lefty and its twin B in Righty. At t, each of them has a
50% chance of
decaying within a year. A’s decay is probabilistically
independent of B’s decay.
Consider the following claims.
A: Particle A decays within a year after t.
B: Particle B decays within a year after t.
24 What was said at the end of section 1 applies here, too.
Those who take anti-individualism to be a
necessary truth deny that there’s a possible world where it’s a
fundamental individualist fact that the chance
that (a) equals p (for some specific individual a). Such
philosophers should agree, however, that there is a
possible world w that meets the following description.
(24) There is some individual a that has such-and-such
qualitative features, such that cht((a)) = p.
(Note that (24) is a purely qualitative claim.) And they can
understand (7) as the thesis that what makes a
claim of the form (24) true at a world is the fact that at that
world,
There is some individual a that has such-and-such qualitative
features, such that that the chance
measure of the set of possible worlds that contain a counterpart
of a that satisfies ‘Φ(x)’ equals p.
My argument applies to this position. To see this, the reader
just needs to understand the letters ‘A’ and ‘B’
in my description of w in (8) below as variables bound by an
existential quantifier, rather than as names for
the two X-bosons.
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16
S0 / S1 / S2: Exactly zero/one/two X-bosons decay within a year
after t.
(I will use ‘A’, ‘B’, ‘S0’, etc. both as abbreviations and as
names for these claims, a
harmless ambiguity. Note that ‘A’ and ‘B’ are not italicized, to
distinguish them from the
italicized letters I am using for the two bosons.)
Let OPt be the set of possible worlds that are like w up to t
and follow the laws of w
thereafter. (Since each world in OPt is like w up to t, each
such world contains two X
bosons at t. And since each world in OPt follows the laws of w
and these laws rule out the
generation of new X bosons, no world in OPt contains more than
these two X bosons at
any time after t.) Given the perfect symmetry of w up to t, and
assuming that the laws of
w are purely qualitative (they don’t mention specific
individuals by name), we can
conclude that any way that Lefty can evolve consistently with
the laws and the history up
to t is also a way that Righty can evolve, and vice versa. So,
for any world w1 in OPt,
there is another world w2, such that
(9) w2 represents Lefty as evolving in just the way w1
represents Righty as evolving,
and w2 represents Righty as evolving in just the way w1
represents Lefty as
evolving.
Where w1 and w2 are any two worlds in OPt that stand to each
other in the relation
described in (9),
(10) w2 represents B as evolving in exactly the way w1
represents A as evolving, and w2
represents A as evolving in exactly the way w1 represents B as
evolving.
Moreover, it follows from (9) that w1 and w2 are qualitatively
indistinguishable. By anti-
haecceitist lights, therefore, w1 and w2 cannot differ in what
they represent concerning
any individual. In particular,
(11) w1 represents A as evolving in exactly the way w2
represents A as evolving, and w1
represents B as evolving in exactly the way w2 represents B as
evolving.
(10) and (11) together entail that w1 represents A as evolving
in exactly the way that w1
represents B as evolving. So, every counterpart of A in w1 is
also a counterpart of B, and
vice versa. That is to say, each of the two X bosons in w1 is a
counterpart of both A and B.
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17
Our argument therefore shows that any X boson in any world in
OPt is a counterpart of
both A and B. That conclusion, as I will argue next, forces some
very unwelcome
consequences on the anti-haecceitist.
(8) stipulates that
(12) cht(A) = cht(B) = cht(B/A) = 50%.
What, then, are the chances of S0, S1, and S2? The answer may
seem obvious:
(13) cht(S0) = cht(S2) = 25%
cht(S1) = 50%
But the anti-haecceitist cannot say this. According to (7),
cht(A) equals the chance
measure of the set of worlds where a counterpart of A decays.
And given that every X
boson in any world in OPt is a counterpart of A, that is just
the set of all worlds in OPt
where at least one X boson decays (the set of worlds where
either S1 or S2 is true). But if
(13) were true, the chance measure of that set would be 75%. So,
by anti-haecceitist
lights, (13) entails that A’s chance of decay is 75%, contrary
to our initial stipulation (as
stated in (12)). The anti-haecceitist therefore cannot accept
what seems to be obvious,
namely that if (12) is true at w, then (13) is true at w as
well.
That’s only the beginning of the anti-haecceitists’ troubles.
They are also forced to
deny that the following compelling principles hold for physical
chance:
(14) P(~A) = 1 – P(A).
(15) P(A or B) = P(A) + P(B), where A and B are mutually
logically inconsistent.
The example of the two bosons illustrates this. Suppose that
cht(S1) > 0. Now, since every
boson in every world in OPt is a counterpart of both A and B, we
can conclude from (7)
that cht(A) = cht(S1) + cht(S2), and that cht(~A) = cht(S0) +
cht(S1). So, cht(A) + cht(~A) =
cht(S0) + 2 × cht(S1) + cht(S2). Since cht(S1) > 0 and
cht(S0) + cht(S1) + cht(S2) = 1, it
follows that cht(A) + cht(~A) > 1, contrary to (14).
Principle (15) fails as well. For
according to (7), cht(A or ~A) is equal to one (since the set of
worlds in OPt where A has
a counterpart that either decays or fails to decay is OPt
itself, and its chance measure is
therefore 1). So, cht(A or ~A) = 1 < cht(A) + cht(~A),
contrary to (15).
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18
It might seem very surprising at first blush that (14) and (15)
fail for chances on the
anti-haecceitist picture. We are used to thinking that both
principles follow from the
axioms of the probability calculus that are often taken to
define the concept of a
probability measure. The anti-haecceitist, however, ought to
deny that (14) and (15)
follow from the probability axioms. The usual set-theoretic
presentation of the probability
calculus appeals to a set of ‘outcomes,’ , and a σ-algebra F
over , that is, a set of
subsets of that includes and is closed under complementation and
countable union
and intersection. When we are concerned with objective physical
chance, is most
naturally taken to be the set of all maximally specific possible
situations, or possible
worlds. (Of course, when we are considering some other notion of
probability, for
example rational credence, we might prefer to interpret
differently, for instance as the
set of centered worlds. I will focus exclusively on chance,
however.) The members of F
can be interpreted as possible (maximal or non-maximal)
situations. Each member of F is
a possible situation that obtains in all and only those possible
worlds that are its members.
(For example, one member X of F might be the set of all and only
those possible worlds
where it will rain tomorrow. Then X is the situation of its
raining tomorrow.) Suppose
that we use ‘P( ) = x’, with italicized ‘P’, for the predicate
‘has chance x’, which is
applicable to members of F, while reserving ‘P( ) = x’, with
non-italicized ‘P’, for the
sentential operator ‘the probability is x that ___.’ Then we can
state Kolmogorov’s
axioms as follows:
(16) (i) P(X) 0 for all X in F.
(ii) P() = 1.
(iii) For any countable sequence X1, X2, … of pairwise disjoint
members of F,
P(X1 X2 …) = P(X1) + P(X2) + … .
Principle (6) connects claims using chance predicates applied to
sets of worlds to
claims containing the sentential chance operators. If we want to
derive (14) and (15) from
(6) and the axioms (16), we need the following principle:
(17) If ‘P’ and ‘Q’ are mutually logically inconsistent, then
there is no possible world
where it is true that P and where it is also true that Q.
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19
The anti-haecceitist counterpart theorist, however, needs to
reject (17). Remember that
for the anti-haecceitist, it’s true at world w that Φ(i) just in
case w contains a counterpart
of i that satisfies ‘Φ(x).’ Now, when a world w contains more
than one counterpart of i,
then one of them may satisfy ‘Φ(x),’ while another satisfies
‘~Φ(x).’ Then it’s true at w
that Φ(i) and it’s also true at w that ~Φ(i). (But it’s not true
at w that Φ(i) & ~Φ(i). That
would be true at w only if w contained a single counterpart of i
that satisfies ‘Φ(x) &
~Φ(x),’ which is obviously impossible.)25
The example of the two bosons illustrates this
state of affairs. It’s true at an S1-world that A decays, since
A has a decaying counterpart
in that world, and it’s also true at that world that A fails to
decay, since A has a non-
decaying counterpart in the world as well. (But it’s not true at
that world that A both
decays and fails to decay, since A doesn’t have counterparts
that both decay and fail to
decay.) Since the anti-haecceitist rejects (17), and since (17)
is needed for the derivation
of principles (14) and (15) from the probability axioms and (6),
the anti-haecceitist will
also reject that derivation.
Is there some easy way in which the anti-haecceitist could
revise principle (7) to get
around the problems outlined in this section? I assumed that
cht(P) equals the chance
measure of the set of worlds that represent that P. I assumed
further that, according to the
anti-haecceitist, a world represents that Φ(a) just in case it
contains some counterpart of a
that satisfies ‘Φ(x).’ Since a single world can contain several
counterparts of a single
object, this account entails that a world can represent that
Φ(a) while at the same time
representing that ~Φ(a). That’s why principles (14) and (15)
fail. Can we fix the problem
by tweaking the account of what it is for a world to represent
that Φ(a)? What about the
following view: u represents that Φ(a) just in case u contains
some counterpart of a and
every counterpart of a that exists in u satisfies ‘Φ(x)’? On
that account, a single world
cannot represent both that Φ(a) and that ~Φ(a). But another,
equally serious problem
25 By anti-haecceitist lights, it’s possible for a world to
represent that Fa and also to represent that ~Fa,
but no world can represent that (Fa & ~Fa). So,
representation by worlds (truth at a world) isn’t closed
under conjunction. Is that an implausible conclusion? As
mentioned in footnote 7, I think that, in the senses
in which I’m using ‘represent’ and ‘truth at a world,’ they may
express concepts different from the ordinary
notions of representation and truth. We should therefore not
expect that we can consult pre-theoretical
intuition to find out how the concepts expressed by the two
terms behave. If it sounds implausible to deny
closure under conjunction, then that may be because we’re
confusing the notions expressed by the two
phrases with the ordinary concepts of representation and truth.
I don’t hold it against anti-haecceitism that it
commits us to denying that truth at a world and representation
by a world are closed under conjunction.
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20
arises now: a world can contain a counterpart of a, but it may
neither represent that Φ(a)
nor that ~Φ(a), since it could be that some counterparts of a in
the world satisfy ‘Φ(x)’
while others satisfy ‘~Φ(x).’ That is indeed the case in the
above example. The S1-worlds
in OPt contain a decaying and a non-decaying counterpart of A.
So, on the new account
these worlds neither represent that A nor that ~A. The S0-worlds
are the only worlds in
OPt that represent that ~A, and the S2-worlds are the only
worlds in OPt that represent
that A. So, if cht(S1) ≠ 0, then cht(A) and cht(~A) don’t sum to
one. (14) still fails. So
does (15). For, even on the new account, cht(A or ~A) = 1, since
every world in OPt
contains a counterpart of A and every counterpart of A in any
world in OPt satisfies ‘x
decays or x fails to decay’. Hence, if cht(S1) ≠ 0, then cht(A
or ~A) = 1 > cht(A) +
cht(~A), contrary to (15).
To avoid the failure of (14) and (15), the anti-haecceitist
needs a theory according to
which every world in OPt represents that A if and only if it
doesn’t represent that ~A.
How would such an account go? Try this. If ‘Φ(a)’ is atomic,
then v represents that Φ(a)
just in case v contains some counterpart of a that satisfies
‘Φ(x).’ Truth at a world can
then be defined recursively for compound sentences in the
obvious way: v represents that
~Φ(a) just in case v does not represent that Φ(a), etc. But that
looks like a non-starter,
since what’s true at a given world now seems to depend on what
the primitive predicates
(and hence the atomic sentences) of the language are. If we
start with ‘decays’ as a
primitive predicate, then ‘A decays’ is atomic. Then ‘A decays’
is true at all worlds in OPt
that contain a decaying counterpart of A, that is, in all S1-
and S2-worlds, and ‘A doesn’t
decay’ is true at all worlds that contain no such counterpart of
A, that is, all S0-worlds.
So, cht(A) = cht(S1) + cht(S2), cht(~A) = cht(S0). If we instead
start with a primitive
predicate ‘F’ that is true of an X boson just in case that boson
continues to exist (doesn’t
decay), then ‘A is F’ is true in all worlds where some
counterpart of A fails to decay, that
is, in all S0- and S1-worlds, while ‘A is not F’ is true in all
S2-worlds. So, cht(A is F) =
cht(S0) + cht(S1) and cht(A is not F) = cht(S2). But that’s
absurd. ‘A is F’ ought to be true
in just those worlds where ‘A doesn’t decay’ is true. cht(A)
ought to equal cht(A is not F)
and cht(~A) ought to equal cht(A is F).
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21
I suspect that no simple revision of principle (7) will solve
the problems for anti-
haecceitism considered in this section. More substantial
revisions will be considered in
section 5.
4. The role of possibilities in the theory of
counterfactuals
4.1 The argument
On the standard view of counterfactuals, which (ignoring some
aspects of it that are
irrelevant to the present topic) I take to be essentially
correct,
(18) A counterfactual ‘P □→ Q’ is true at possible world u just
in case Q is true at all
the possible P-worlds that are closest (most similar overall) to
u.26
I will argue that this account yields unacceptable predictions
unless we endorse a
haecceitist account of possible worlds.
An example will help to bring this out. Let w be a possible
world that is
indeterministic and, before time t, perfectly symmetrical. (By
sheer coincidence, all
chance processes before t have the same outcomes in the two
halves of the universe.)
Fred lives in one half of the universe. Twin-Fred, who is
qualitatively indistinguishable
from Fred before t, lives in the other half. Fred and Twin-Fred
are both professional
contortionists, and they are the only ones in the history of w.
At t, the two halves of the
universe diverge from one another. At that moment, Fred and
Twin-Fred are both
deciding whether to have tea or coffee for breakfast. Fred
decides to go for coffee, while
Twin-Fred chooses tea. Both decisions are genuinely
indeterministic. The difference in
their breakfasts causes a few other differences later on. For
example, there is a used tea
bag in Twin-Fred’s garbage, but not in Fred’s. But let’s suppose
that the events that are
causally unaffected by the choice of breakfast drinks are
exactly alike in the two halves
of the universe.
In w, it’s surely true that
26 This theoretical framework is due to Stalnaker (1968) and
Lewis (1973). Other significant work done
in this framework includes Jackson (1977), Bennett (1984, 2003),
and Lewis (1986a), in addition to the
writings mentioned later on in this paper.
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22
(19) If Fred had chosen tea rather than coffee, then there would
have been two tea-
drinking contortionists immediately after t.
To make this entirely clear, suppose that God foreordained that
the world will instantly
become a paradise if there are at least two tea-drinking
contortionists immediately after t.
Upon hearing this and finding out that Twin-Fred had tea, Fred
might exclaim:
Oh no! If only I had had tea! Then there would have been two
tea-drinking
contortionists and we would be living in paradise.
Surely, Fred is right.
The same conclusion can be made plausible in other ways, too.
After all, there is no
causal connection between Fred’s decision about what to drink
and Twin-Fred’s
simultaneous decision. (The two events occur at the same time in
different places, and
let’s suppose that in w no causal signal can travel
instantaneously.) It therefore seems that
Twin-Fred would have made the same decision if Fred’s decision
had been different. So,
if Fred had chosen tea, there would have been two tea-drinking
contortionists.27
The anti-haecceitist cannot accommodate our impression that (19)
is true. My
argument for this conclusion will rest on two premises.
a. Twin-Fred is a counterpart of Fred.
The counterpart theorist cannot plausibly deny this. Let
PTwin-Fred be the conjunction of all
the purely qualitative properties that Twin-Fred has in w,
including relational properties,
negative properties, etc. (The statement that someone has this
property constitutes a
complete description of all qualitative features of the world.)
It seems undeniable that
(20) It’s (metaphysically) possible that Fred has
PTwin-Fred.
After all, all it would have taken for Fred to have PTwin-Fred
is for each of the two
contortionists to choose a different breakfast drink. And before
time t, there was a non-
zero chance that exactly that would happen. So, surely it could
have happened. That
27 For a defense of the principle that, roughly speaking, all
matters of particular fact that are causally
independent of the antecedent-event should be held fixed in
counterfactual reasoning, see Adams (1975, ch.
4, sct. 8, in particular 132f.), Edgington (2003), Mårtensson
(1999), Bennett (2003, ch. 15), Schaffer
(2004), Hiddleston (2005), Kment (2006), and Wasserman
(2006).
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23
means that there is a possible world that represents Fred as
having PTwin-Fred. But such a
world is qualitatively indistinguishable from w, and by
anti-haecceitist lights, there are no
qualitatively indistinguishable worlds that differ in what’s
true at them concerning
specific individuals. Hence, w itself must represent Fred as
having PTwin-Fred. That’s to
say, w must contain a counterpart of Fred who has PTwin-Fred.
But that can only be Twin-
Fred, since Twin-Fred is the only denizen of w who has
PTwin-Fred. So, Twin-Fred must be
a counterpart of Fred.28, 29
b. Weak Centering
That’s the assumption that every world is at least as close to
itself as any other world is to
it. This assumption is not to be confused with the principle of
Strong Centering,
according to which every world is closer to itself than any
other world is to it. Weak
Centering, in contrast to Strong Centering, allows for the
possibility that a world u is tied
with other worlds for the title of world that is closest to u.
While some philosophers have
objected to Strong Centering, Weak Centering seems to be widely
accepted.30
In fact,
Weak Centering may seem self-evident. How could a world be more
similar overall to u
than u is to itself?
Now consider counterfactual (19) again. By anti-haecceitist
lights, (19) is true just in case
all the worlds closest to w where a counterpart of Fred has tea
contain two tea-drinking
contortionists. But since Twin-Fred is a counterpart of Fred, w
itself contains a
28 In his (1968, 114, Postulate P5), Lewis denies that it is
possible for an individual to be a counterpart both of itself and
of another individual in the same world, but it seems to me that
the argument just given
shows this view to be indefensible (and Lewis himself eventually
changed his view on the matter; see, for
example, Lewis (1986b, ch. 4).
29
Recall that on Lewis’s definition, an individual x in world v
can be a counterpart of y only if there is
nothing else in v that is more qualitatively similar overall to
y than x is. How, then, can Twin-Fred be a
counterpart of Fred on Lewis’s definition? Isn’t there something
in w that is more similar to Fred than
Twin-Fred, namely Fred?
In response, the anti-haecceitist can point out that the
relation of overall similarity used to define the
counterpart relation rests on a different method of weighting
similarities than our offhand judgments about
overall similarity. (See Lewis (1986a), where Lewis makes the
same point about the relation of overall
similarity used in defining the counterfactual conditional.) The
rules defining the counterpart relation may
assign zero weight to some respects of similarity. In our
example, for instance, the similarities that Fred has
to himself but not to Twin-Fred may carry no weight whatsoever,
so that Twin-Fred counts as being as
similar to Fred as Fred is to himself. (See section 4.2 for more
discussion of this point.)
30
The principles of Strong and Weak Centering are discussed in
Lewis (1973). See Bennett (2003) for
an argument against Strong Centering.
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24
counterpart of Fred who has tea. And by Weak Centering, w is one
of the worlds closest
to w that satisfy this condition. But w contains only one
tea-drinking contortionist. So,
(19) is false at w. The anti-haecceitist needs to say that it’s
true at w that, if Fred had had
tea, then there might still have been only one tea-drinking
contortionist.31
No similar problem arises for the haecceitist. In contrast to
the anti-haecceitist, the
haecceitist doesn’t believe that it’s true at w that Fred has
tea. There is indeed a world
qualitatively exactly like w where Fred has tea, but that world
is distinct from w. And it’s
not among the worlds closest to w where Fred has tea. The
closest such worlds are those
where everything that is causally unaffected by Fred’s decision
about his breakfast drink
is just the way it is in w. In particular, in the closest worlds
where Fred has tea, Twin-
Fred still chooses tea.32
In these worlds, there are two tea-drinking contortionists (and
the
world turns into paradise). So, by haecceitist lights, (19) is
true at w.
4.2 An anti-haecceitist reply: context-dependence
It is time to consider a reply that the anti-haecceitist reader
has been waiting impatiently
to make while reading the last section. The standards of
similarity that govern the
counterpart relation are usually regarded as context-sensitive.
Consider
(21) The bronze picture frame in my study could have been a
vase.
That sentence may be true in one context but false in another.
In the first context, we are
using a counterpart relation that is permissive enough to count
certain otherworldly vases
as counterparts of the frame. In the second context, the
conditions for counterparthood
are stricter, so that no otherworldly vases are counterparts of
the frame. In the course of a
conversation, the standards of similarity can change, for
example by the rule of
accommodation. As soon as you utter (21), your audience, if
cooperative, will change the
31 I am following David Lewis (1973, 21) in using ‘If P had been
the case, then Q might have been the
case’ as equivalent to ‘it’s not the case that if P had been the
case, then Q would not have been the case,’
that is, as roughly equivalent to the claim that the closest
P-worlds include some Q-worlds.
32
On this view, then, some of the worlds that are qualitatively
indistinguishable from w (namely those
where Fred and Twin-Fred swap qualitative roles) are less close
to w than some worlds that differ
qualitatively from w (namely those where both contortionists
have tea). That shows that closeness isn’t
purely a matter of qualitative similarity. It also matters to
the degree of closeness between two worlds how
similar they are with respect to the way qualitative properties
and relations are distributed over specific
individuals.
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25
standards of similarity to turn the otherworldly vase into a
counterpart of our worldmate,
the frame.
My argument in the last section started from the assumption that
(20) is true. I
concluded that Twin-Fred must be a counterpart of Fred. Then I
used that result to draw
conclusions about what the anti-haecceitist has to say about
(19). At this point, anti-
haecceitists might complain that I have overlooked the
possibility that the standards of
similarity that define the counterpart relation change when we
shift our attention from
(20) to (19). And anti-haecceitists could try to appeal to such
a shift to explain away the
apparent counterexample. To be more concrete, they could argue
as follows:
When we consider (20), Twin-Fred counts as a counterpart of
Fred, which is why
(20) is true. When we then go on to consider (19), however,
Twin-Fred no longer
counts as Fred’s counterpart, and w (the world of the example)
therefore doesn’t
count as containing a tea-drinking counterpart of Fred. w
consequently doesn’t
count as an antecedent-world, and hence doesn’t count as one of
the antecedent-
worlds closest to w. Instead, the closest antecedent-world is a
world (call it ‘w2tea’)
that is just like w before t and where both contortionists then
have tea. That’s why
(19) is true at w.
Call the two tea-drinking contortionists in w2tea ‘Ed’ and
‘Twin-Ed.’ The anti-
haecceitist’s proposal assumes that Twin-Fred is a counterpart
of Fred in a context where
we consider (20), while in a context where we consider (19), Ed
and Twin-Ed are
counterparts of Fred, while Twin-Fred isn’t. Let’s consider how
this proposal could be
worked out. Suppose first that the anti-haecceitist endorses
Lewis’s definition of the
counterpart relation: x in world u is a counterpart of y just in
case x meets certain
minimum standards of similarity to y and nothing in u is more
similar to y than x is. The
two clauses of this definition give us two possible explanations
of how the shift in the
extension of the counterpart relation proposed by the
anti-haecceitist could have come
about.
Explanation 1. In the context where we consider (20), Twin-Fred
has the minimum
degree of similarity to Fred required to be his counterpart.
When we turn our attention
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26
to (19), the minimum requirements increase and while Ed and
Twin-Ed meet the new
minimum requirements, Twin-Fred doesn’t.
Ed and Twin-Ed differ from Fred in their choice of breakfast
drink and its consequences,
but are otherwise qualitatively indistinguishable from Fred in
every way. Twin-Fred
differs from Fred in the same ways, but there’s an additional
difference as well: while
Fred has a tea-drinking twin off in a distant corner of the
universe (and the same is true of
Ed and Twin-Ed), Twin-Fred has a coffee-drinking twin. As far as
I can see, that is the
only way in which Ed and Twin-Ed are more similar to Fred than
Twin-Fred is. It is this
extra similarity to which the anti-haecceitist who gives
Explanation 1 must appeal. In the
context where we consider (19), Ed and Twin-Ed are only just
similar enough to Fred to
count as his counterparts. Twin-Fred, having an extra
dissimilarity from Fred, is below
the threshold. In the context where we consider (20), by
contrast, the minimum
requirements for counterparthood are lower, and Twin-Fred still
counts as a counterpart
of Fred.
The second explanation of the contextual shift appeals to the
fact that, in order to be a
counterpart of Fred by Lewis’s definition of counterparthood,
Twin-Fred must not have a
worldmate who is more similar to Fred than he (Twin-Fred) is.
Whether Twin-Fred meets
this condition depends on whether Fred counts as more similar
overall to himself than
Twin-Fred is to Fred. That, in turn, depends on the specific
standards of overall similarity
that are in force in the context, that is, on the specific
method of weighting the different
respects of similarity. And these standards can change. Hence,
we get
Explanation 2. By the standards of similarity that are relevant
in the context
where we consider (20), Twin-Fred counts as being as similar to
Fred as Fred is to
himself. By the standards in force when we consider (19), he
counts as less
similar to Fred than Fred is to himself.
Fred, of course, is similar to himself in some ways in which
Twin-Fred is not similar to
him, namely in his choice of breakfast drink and its
consequences, and in having a tea-
drinking twin. In the context where we consider (20), these
similarities enter the scales
with zero weight. Fred and Twin-Fred come out as equally similar
overall to Fred, and
Twin-Fred is therefore a counterpart of Fred. When we consider
(19), by contrast, the
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27
same similarities carry non-zero weight, so that Twin-Fred
counts as less similar to Fred
than Fred is to himself. Twin-Fred no longer counts as a
counterpart of Fred.
These two explanations rested on Lewis’s definition of
counterparthood. The anti-
haecceitist, of course, might prefer the simpler alternative
definition considered in section
2, which simply omits the second clause of Lewis’s definition.
According to this
definition, x is a counterpart of y if and only if x is
sufficiently similar to y. Endorsing that
definition does not, however, put the anti-haecceitist in a
better position to answer the
challenge. On the contrary, the only effect is to make
Explanation 2 unavailable, leaving
the anti-haecceitist with Explanation 1 as the sole option.
So much about the two changes in the standards of similarity
that anti-haecceitists
could postulate to explain the phenomena. It seems to me,
however, that the hypothesis
that the standards shift in one of these ways is entirely ad hoc
as long as no independent
reason can be given for believing it. I don’t know of any such
reason. What is more, anti-
haecceitists who believe in the shift owe us an account of the
mechanism that generated
it. They need to explain what underlying changes in the
contextual parameters prompted
the shift, and what the pragmatic rules are that ordain that
these changes affect the
standards of similarity in the ways described. Without such an
account, anti-haecceitists
are not able to predict or explain the shift, and their account
therefore cannot predict or
explain our judgments about the relevant modal claims. But
surely, predicting and
explaining our judgments about the likes of (19) and (20) are
two of the principal
purposes of an account of modal claims.
What is more, there are strong reasons for doubting the
anti-haecceitist’s claim that in
the context where we consider (19), Twin-Fred doesn’t count as a
counterpart of Fred. I
suspect that the anti-haecceitist cannot plausibly say that
there is any context in which
that is true. Note that in any context in which Twin-Fred fails
to count as a counterpart of
Fred, it would be true that
(22) It is (metaphysically) impossible for Fred to have
PTwin-Fred.
But (22) simply sounds false. All it would have taken for Fred
to have PTwin-Fred is for
Fred and Twin-Fred each to choose a different breakfast drink.
And surely that’s
metaphysically possible! After all, it seems that just before
their breakfasts there was a
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28
non-zero chance that it would happen. I don’t know how to create
a context in which (22)
sounds even remotely plausible. But that would be hard to
explain if the anti-haecceitist
were right in thinking that the counterpart relation is flexible
enough to allow for contexts
in which Twin-Fred fails to be a counterpart of Fred. If the
counterpart relation is that
flexible, then why can’t we create a context where (22) is true
simply by uttering (22) and
relying on our audience to apply the rule of accommodation? It
seems to me that the
simplest and most plausible explanation for the fact that (22)
never sounds true is that it is
false in every context. Counterpart theorists can allow the
counterpart relation to vary
across contexts, but only within limits. They cannot allow for a
context where someone
as similar to Fred as Twin-Fred fails to be Fred’s
counterpart.
5. Anti-haecceitist replies
I will discuss two very natural responses that an
anti-haecceitist might make to the
problems discussed in sections 3 and 4. Both strategies reject
principles (6) and (18) and
offer replacements. As we will see, essentially the same
objection applies to both of
them. I suspect that the difficulty generalizes to other
attempted fixes of anti-haecceitism
that may be proposed.
5.1 World description theory
I argued that to get the right predictions about chance and
counterfactuals, we have to
accept that there are pairs of qualitatively indistinguishable
worlds that differ in what
they represent about specific individuals. Only haecceitists
allow for such pairs.
However, whenever haecceitists distinguish between two different
worlds that are
qualitatively indistinguishable but differ in what they
represent about specific individuals,
anti-haecceitists distinguish between different ways of
describing a single world. These
different descriptions correspond to different mappings from
individuals in that world to
their counterparts. And anti-haecceitists may try to exploit
that distinction for the same
purposes for which haecceitists use their distinction between
qualitatively
indistinguishable worlds that represent different things about
specific individuals.
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29
As a first step, anti-haecceitists can define what they may call
‘possible world
descriptions.’ A possible world description is an ordered pair
consisting of a possible
world u and a (possibly partial) function from individuals in u
to individuals that are their
counterparts. In addition to the familiar notion of truth at a
world, we can define the
notion of a claim’s being true at a world description. A purely
qualitative claim is true at
a world description just in case it is true at world u. A claim
about a specific
individual, let’s say the claim that a is P, is true at a world
description just in case,
where b is the individual in u to which f assigns a, b is P.
The anti-haecceitist can then define the chance measure, not on
the set of possible
worlds, but on the set of possible world descriptions. cht(P)
equals the measure of the set
of world descriptions where P is true. Similarly, the world
descriptions, not the worlds,
are the relata of the closeness relation. If we call a world
description where the claim P is
true a ‘P-world description,’ we can say that a counterfactual
‘P □→ Q’ is true at world
description u just in case Q is true in all those P-world
descriptions that are closest to u.
The principle of Weak Centering can be reformulated as the
principle that any world
description u is at least as close to u as any other world
description is to u.
Call the theory just stated ‘world description theory.’ World
description theory can
solve the problem cases of sections 3 and 4 without difficulty.
In the X boson example,
there are two different sets of world descriptions corresponding
to the set of possible
worlds in OPt where exactly one particle decays. One of these
sets includes only world
descriptions that map the decaying particle to A and the
non-decaying one to B, the other
includes the world descriptions with the opposite mapping. The
chance measure of each
of these sets of world descriptions is 25%. The set of world
descriptions where both
particles decay also has a 25% chance, as does the set of world
descriptions where neither
particle decays. This chance measure yields the intuitively
correct results. In particular,
cht(A) = cht(B) = cht(B/A) = 50%. cht(S0) = cht(S2) = 25%.
cht(S1) = 50%. And since
every world description corresponding to a world in OPt
represents A either as decaying
or as not decaying, but not both, cht(~A) = 1 – cht(A).
Consider next the case of world w described in section 4.1,
which is inhabited by the
two contortionists. There are two relevant world descriptions
that have w as their first
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30
member: the pair consisting of w and the identity mapping on the
individuals in w,
and a world description that differs from the latter by mapping
Fred to Twin-Fred
and Twin-Fred to Fred. By Weak Centering, is as close to as any
world
description is to . World description is farther away from than
a
world description where both contortionists have tea. (19) comes
out true.
My brief sketch of world description theory underspecifies the
view in a number of
ways, but there is no need to develop the account any further,
as the main problem for the
theory is independent of the details. Let me explain. While the
expression ‘possible
world’ may be a technical term, it seems plausible to me that
the concept it expresses is
familiar from non-philosophical contexts. Roughly speaking, it
is the notion of a
(maximally specific) way things could be. We have various
beliefs about ways things
could be before we enter the philosophy room. I happen to think
that (6) and (18) are
nothing more than philosophically sophisticated versions of such
pre-philosophical
beliefs. That is bound to be very controversial in the case of
(18) (and I cannot argue for
the claim here). But it seems very plausible in the case of (6),
even in the absence of a
detailed argument. It’s very natural to think that, when we talk
about the chance that a
certain way for the world to be had on Sunday. (6) is simply a
more precise statement of
this thought.
Let us assume, then, that at least one of (6) and (18) is a
version of a principle that is
part of the folk theory about ways things could be. Now,
according to world-description
theorists, neither (6) nor (18) is true of the entities they
call ‘worlds’; both claims hold of
world descriptions instead. That means that the entities they
call ‘worlds’ don’t play the
role we associate with worlds pre-philosophically. That role is
taken over by the world
descriptions. But it seems plausible that what entities our
thoughts and utterances about
worlds (or about ways things could have been) are about is
determined in large part by
the (folk-)theoretical role associated with the concept of a
world. If the entities that best
fit this role are the world descriptions, then, other things
being equal, these entities are
better candidates for being the referents of ‘world’ than the
entities which the world
description theorists call ‘worlds.’ So, world description
theorists seem simply to be
misdescribing their own account. If their view is correct, then
the world descriptions are
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31
really the possible worlds (they are the things we are talking
about when we speak of
ways things could be). But world descriptions satisfy the
haecceitist’s conception of
worlds, not the anti-haecceitist’s. For clearly, there can be
world descriptions where the
same qualitative claims are true, but where different claims
about specific individuals
hold. World description theory, when correctly described, turns
out to be a version of
haecceitism.
There are a few ways for world description theorists to respond.
For a start, they could
deny that any version of either (6) or (18) is part of folk
theory about ways things could
be, or that folk theory really plays such an important role in
determining the reference of
‘world.’ I don’t myself find these responses plausible, and will
instead focus on a
different reply the world description theorist may give, which
exploits a loophole in the
foregoing argument. I said: since the world descriptions fit the
(folk-)theoretical role of
worlds better than the entities which the world description
theorist calls ‘worlds,’ the
world descriptions are better candidates for being the referents
of ‘world,’ other things
being equal. But world description theorists may argue that
other things are not equal.
Following Lewis, they may claim that satisfying the theoretical
role is only one
desideratum for candidate referents of ‘world.’ It needs to be
weighed against the
desideratum of naturalness.33
And perhaps world description theorists can present an
account of what they call ‘worlds’ that makes it plausible that
these entities are, on
account of their greater naturalness, significantly more
eligible candidates for being the
referents of ‘world’ than world descriptions.
For an illustration of how this line could be developed,
consider Lewisian modal
realism. If Lewisian worlds existed, they would be very natural
subdivisions of reality,
and they would be a more natural kind of thing than pairs
consisting of a Lewisian world
and a mapping of its constituent individuals to certain of their
counterparts. From the
Lewisian perspective, therefore, we could argue that ‘world’
refers to Lewisian worlds,
rather than to world descriptions, even if the latter fit the
theoretical role of worlds better.
This specific version of world description theory is unlikely to
appeal to many anti-
haecceitists, given the implausibility of Lewisian realism. (Not
only does this view carry
33
Lewis 1983, 1984.
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32
dubious ontological commitments and offend widely shared
actualist sentiments, but
modal realism seems even less plausible once we realize that
Lewisian worlds satisfy the
theoretical role of worlds only imperfectly, for then the
account necessitates revisions in
our view of worlds.) What if we jettison modal realism in favor
of an ersatzist conception
of worlds? In that case, it is less obvious how to argue that
worlds are decisively more
natural than world descriptions. Consider, for example, a
linguistic ersatzist who claims
that a world is an infinitely complex Ramsey sentence, while a
world description is a pair
consisting of a Ramsey sentence u and an assignment of its
constituent individuals (that
is, centered worlds ) to other individuals. Admittedly, on this
view world
descriptions are slightly more complex set-theoretic
constructions than the worlds
themselves, and are therefore perhaps a little bit less natural.
But it would be implausible
to hold that this very small difference in naturalness by itself
makes worlds so much more
natural than world descriptions that it outweighs the fact that
the world descriptions
satisfy th